Why do original legs have orange dots, but mirrored ones do not?
The orange dots are the object origins of the selected objects. It looks like you have created multiple armature objects, one for each leg.

You only want one armature object for the spider, then add multiple bones to the armature while in edit mode. This allows you to move the entire spider as one while moving individual parts in pose mode as needed.

You can select multiple armature objects and merge them into one by pressing &#9096; CtrlJ